%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU857^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:34:18 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 7
% Syntax : Number of formulae : 176 ( 16 unt; 0 typ; 6 def)
% Number of atoms : 2403 ( 530 equ; 0 cnn)
% Maximal formula atoms : 6 ( 13 avg)
% Number of connectives : 3257 ( 655 ~; 690 |; 571 &;1335 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 35 ( 0 sgn 12 !; 3 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vNOT: $o > $o ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_6,type,
sK0: a > $o ).
thf(func_def_7,type,
sK1: a > $o ).
thf(func_def_8,type,
sK2: a > $o ).
thf(func_def_11,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) )
| ( ~ ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGAZING_THM43_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) ) )
= ( ^ [X3: a] :
( ( ~ ( X0 @ X3 )
& ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) ) )
| ( ~ ( ( ~ ( X1 @ X3 )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( X1 @ X3 ) ) )
& ( X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [X3: a] :
( ( ~ ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
& ( X2 @ X3 ) )
| ( ~ ( X2 @ X3 )
& ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) ) ) ) )
= ( ^ [X4: a] :
( ( ~ ( X0 @ X4 )
& ( ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) )
| ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) ) ) )
| ( ~ ( ( ~ ( X1 @ X4 )
& ( X2 @ X4 ) )
| ( ~ ( X2 @ X4 )
& ( X1 @ X4 ) ) )
& ( X0 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
| ( ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ^ [Y0: a] :
( ( ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( ( ( X0 @ Y0 )
& ~ ( X1 @ Y0 ) )
| ( ( X1 @ Y0 )
& ~ ( X0 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ~ ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) ) )
| ( ( ( ( X1 @ Y0 )
& ~ ( X2 @ Y0 ) )
| ( ( X2 @ Y0 )
& ~ ( X1 @ Y0 ) ) )
& ~ ( X0 @ Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ^ [Y0: a] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,plain,
( ( ^ [Y0: a] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f7]) ).
thf(f18,plain,
( ( $true
= ( ^ [Y0: a] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK1 @ Y0 )
& ~ ( sK0 @ Y0 ) ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ~ ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) ) )
| ( ( ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) )
| ( ( sK2 @ Y0 )
& ~ ( sK1 @ Y0 ) ) )
& ~ ( sK0 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( $false
= ( ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
( ( $false
= ( ( sK2 @ sK3 )
& ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f22,plain,
( ( $false
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f20]) ).
thf(f23,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f24,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f24]) ).
thf(f27,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f27]) ).
thf(f29,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f29]) ).
thf(f33,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f33]) ).
thf(f35,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f34]) ).
thf(f37,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f35]) ).
thf(f38,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f37]) ).
thf(f65,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f66,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f65]) ).
thf(f67,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f79,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f80,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f82,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f82]) ).
thf(f84,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f84]) ).
thf(f89,plain,
( ( $false
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f90,plain,
( ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f93]) ).
thf(f128,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f128]) ).
thf(f131,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f129]) ).
thf(f132,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f131]) ).
thf(f137,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f132]) ).
thf(f138,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f137]) ).
thf(f139,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f138]) ).
thf(f149,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f92]) ).
thf(f151,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f149]) ).
thf(f152,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f154]) ).
thf(f170,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f171,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f178,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f179,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f182,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f183,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f182]) ).
thf(f205,plain,
( ( $true
= ( ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f206,plain,
( ( $true
= ( ( sK2 @ sK3 )
& ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $true
= ( ~ ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f216,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f217]) ).
thf(f221,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f219]) ).
thf(f223,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f225,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f225]) ).
thf(f469,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f471,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f469]) ).
thf(f472,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f471]) ).
thf(f473,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f472]) ).
thf(f498,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f473]) ).
thf(f499,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f498]) ).
thf(f506,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f499]) ).
thf(f508,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f506]) ).
thf(f509,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f508]) ).
thf(f510,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f509]) ).
thf(f511,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f510]) ).
thf(f514,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f511]) ).
thf(f515,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f514]) ).
thf(f535,plain,
( ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f536,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f535]) ).
thf(f537,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f535]) ).
thf(f538,plain,
( ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f537]) ).
thf(f539,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f538]) ).
thf(f540,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f539]) ).
thf(f541,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f540]) ).
thf(f801,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f541]) ).
thf(f802,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f801]) ).
thf(f856,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f802]) ).
thf(f857,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f856]) ).
thf(f860,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f857]) ).
thf(f861,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f860]) ).
thf(f866,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f861]) ).
thf(f867,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f866]) ).
thf(f868,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f867]) ).
thf(f869,plain,
( ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f536]) ).
thf(f870,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f869]) ).
thf(f871,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
& ~ ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f870]) ).
thf(f873,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f871]) ).
thf(f874,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f873]) ).
thf(f875,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f874]) ).
thf(f1004,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK1 @ sK3 )
& ~ ( sK0 @ sK3 ) ) )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f875]) ).
thf(f1005,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1004]) ).
thf(f1107,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) )
| ( ( sK2 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f1005]) ).
thf(f1109,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1107]) ).
thf(f1110,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f1109]) ).
thf(f1113,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f1110]) ).
thf(f1114,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f1113]) ).
thf(f1201,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f1203,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f1201]) ).
thf(f1205,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f1207,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f1205]) ).
thf(f1209,definition,
( spl4_3
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f1211,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1209]) ).
thf(f1212,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f38,f1209,f1205,f1201]) ).
thf(f1214,definition,
( spl4_4
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f1216,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f1214]) ).
thf(f1218,definition,
( spl4_5
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f1220,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f1218]) ).
thf(f1221,plain,
( spl4_4
| spl4_5
| spl4_3 ),
inference(avatar_split_clause,[],[f85,f1209,f1218,f1214]) ).
thf(f1223,definition,
( spl4_6
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f1225,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f1223]) ).
thf(f1226,plain,
( spl4_6
| spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f139,f1205,f1218,f1223]) ).
thf(f1227,plain,
( spl4_6
| spl4_4
| spl4_1 ),
inference(avatar_split_clause,[],[f183,f1201,f1214,f1223]) ).
thf(f1228,plain,
( spl4_5
| spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f226,f1209,f1205,f1218]) ).
thf(f1229,plain,
( spl4_4
| spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f515,f1209,f1201,f1214]) ).
thf(f1230,plain,
( spl4_6
| spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f868,f1205,f1201,f1223]) ).
thf(f1231,plain,
( spl4_6
| spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f1114,f1218,f1214,f1223]) ).
thf(f1234,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f1207,f1216]) ).
thf(f1235,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f1216,f1207]) ).
thf(f1236,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1235]) ).
thf(f1237,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1236]) ).
thf(f1238,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f1234]) ).
thf(f1239,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f1238]) ).
thf(f1241,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f1220,f1203]) ).
thf(f1242,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f1241]) ).
thf(f1243,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f1242]) ).
thf(f1248,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1225,f1211]) ).
thf(f1249,plain,
( ( $true = $false )
| ~ spl4_3
| ~ spl4_6 ),
inference(constrained_superposition,[],[f1211,f1225]) ).
thf(f1250,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1249]) ).
thf(f1251,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1250]) ).
thf(f1252,plain,
( $false
| ~ spl4_3
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1253,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f1252]) ).
cnf(s1,plain,
( spl4_1
| spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f1212]) ).
cnf(s2,plain,
( spl4_3
| spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f1221]) ).
cnf(s3,plain,
( spl4_2
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1226]) ).
cnf(s4,plain,
( spl4_1
| spl4_4
| spl4_6 ),
inference(sat_conversion,[],[f1227]) ).
cnf(s5,plain,
( spl4_2
| spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s6,plain,
( spl4_1
| spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s7,plain,
( spl4_1
| spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f1230]) ).
cnf(s8,plain,
( spl4_4
| spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f1231]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f1237]) ).
cnf(s10,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f1239]) ).
cnf(s11,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f1243]) ).
cnf(s12,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s13,plain,
( ~ spl4_3
| ~ spl4_6 ),
inference(sat_conversion,[],[f1253]) ).
cnf(s14,plain,
( spl4_2
| spl4_1 ),
inference(rat,[],[s12,s1,s7]) ).
cnf(s15,plain,
( spl4_4
| spl4_1 ),
inference(rat,[],[s12,s6,s4]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s15,s10,s14]) ).
cnf(s17,plain,
~ spl4_5,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl4_6,
inference(rat,[],[s9,s3,s8,s17]) ).
cnf(s19,plain,
~ spl4_3,
inference(rat,[],[s13,s18]) ).
cnf(s20,plain,
spl4_4,
inference(rat,[],[s2,s17,s19]) ).
cnf(s21,plain,
spl4_2,
inference(rat,[],[s5,s17,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s9,s20,s21]) ).
thf(f1255,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU857^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n019.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:40:18 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (873143)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (873158)% WARNING: option uhcvi not known.
% 0.08/0.26 % (873157)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2601321499_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.26 % (873158)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1127831690:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (873161)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=349301988:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (873161)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (873158)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (873163)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2133494844:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.26 % (873158)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % Exception at run slice level
% 0.08/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.26 % (873159)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2320245789:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (873162)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1057744329:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (873160)dis+10_1_sil=32000:sp=arity:random_seed=3966408377:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.26 % (873161) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-873143-873161"...
% 0.08/0.26 % (873161)...printing done.
% 0.08/0.26 % (873158) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-873143-873158"...
% 0.08/0.26 % (873161)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.27 % (873161)------------------------------
% 0.08/0.27 % (873161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (873161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (873161)CaDiCaL version: 2.1.3
% 0.08/0.27 % (873161)Termination reason: Refutation
% 0.08/0.27 % (873161)Time elapsed: 0.009 s
% 0.08/0.27 % (873161)Peak memory usage: 13 MB
% 0.08/0.27 % (873161)Instructions burned: 38 (million)
% 0.08/0.27 % (873143)Success in time 0.053 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------